Floquet engineering the Hofstadter butterfly in the square lattice and its effective Hamiltonian

Zhao, Ming; Chen, Qi; Tian, Xue-Dong; Du, Liang

doi:10.48550/arxiv.2007.01071

Cited by 1 publication

(2 citation statements)

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“…This is consistent with the results of Refs. [30,31] where the full Hofstadter butterfly spectrum (tight-binding model) was analyzed. Finally, we mention that the series of gaps near Ω/2 arises from the anti-crossings between the Floquet states |χ nk , 0 and |χ 1−n,k , 1 with n = 1, 2, • • • , while those near − Ω/2 appear at the crossings of |χ −nk , 0 and |χ n+1,k , −1 .…”

Section: Bulk Selection Rulesmentioning

confidence: 99%

“…Here we address the question of how the QH effect in graphene is affected by laser illumination. Previous studies have mainly focused on the effect of light on the intricacies of the Hofstadter butterfly of different lattices [28][29][30][31], the bulk properties of the irradiated Landau levels and topological invariants [28], and related dynamics [32]. By computing the spectrum and the topological invariants, laser-induced modifications on the Hofstadter butterfly and topological properties were recognized.…”

Section: Introductionmentioning

confidence: 99%

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Quantum Hall edge states under periodic driving: a Floquet induced chirality switch

Huamán,

Torres,

Balseiro

et al. 2020

Preprint

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We report on the fate of the quantum Hall effect in graphene under strong laser illumination. By using Floquet theory combined with both a low energy description and full tight-binding models, we clarify the selection rules, the quasienergy band structure, as well as their connection with the two-terminal and multi-terminal conductance in a device setup as relevant for experiments. We show that the well-known dynamical gaps that appear in the Floquet spectrum at ± Ω/2 lead to a switch-off of the quantum Hall edge transport for different edge terminations except for the armchair one, where two terms cancel out exactly. More interestingly, we show that near the Dirac point changing the laser polarization (circular right or circular left) controls the Hall conductance, by allowing to switch it on or off, or even by flipping its sign, thereby reversing the chirality of the edge states. This might lead to new avenues to fully control topologically protected transport.

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Section: Bulk Selection Rulesmentioning

confidence: 99%